1. Field of the Invention
The present invention relates to a differential amplifier circuit comprised of bipolar transistors and more particularly, to an operational transconductance amplifier using bipolar transistors, which has an improved signal-to-noise ratio (S/N) and which is suitable for a semiconductor integrated circuit (IC), and an output circuit used for the amplifier.
2. Description of the Prior Art
A differential amplifier circuit having a superior transconductance linearity within a comparatively wide input voltage range has been known as an "Operational Transconductance Amplifier (OTA)".
A conventional bipolar OTA is shown in FIG. 1, which is termed the "Gilbert gain cell,". This conventional OTA was disclosed in IEEE Journal of Solid-State Circuits, Vol. SC-3, No. 4, December 1968, which was written by B. Gilbert.
As shown in FIG. 1, a first balanced differential pair is formed by two npn bipolar transistors Q101 and Q102. An emitter of the transistor Q101 is connected to one terminal of a constant current sink 101 sinking a constant current I.sub.0. An emitter of the transistor Q102 is connected to one terminal of another constant current sink 102 sinking the same constant current I.sub.0 as that of the current sink 101 for the transistor Q101. The other terminals of the two current sinks 101 and 102 are connected to the ground. The two transistors Q101 and Q102 are driven by the corresponding current sinks 101 and 102, respectively.
The emitters of the transistors Q101 and Q102 are coupled together through a common emitter resistor R101 having a resistance R.
A differential input voltage V.sub.i as an input signal to the conventional OTA is applied across bases of the transistors Q101 and Q102.
Two diode-connected npn bipolar transistors Q103 and Q104 are provided to serve as loads of the transistors Q101 and Q102, respectively. Specifically, emitters of the transistors Q103 and Q104 are connected to collectors of the transistors Q101 and Q102, respectively. A bass and a collector of the transistor Q103 are coupled together to be applied with a power supply voltage V.sub.CC. A base and a collector of the transistor Q104 are coupled together to be applied with the same power supply voltage V.sub.CC.
A second balanced differential pair is formed by two npn bipolar transistors Q105 and Q106. Emitters of the transistors Q105 and Q106 are coupled together to be connected to one terminal of a constant current sink 103 sinking a constant current I.sub.1. The other terminal of the current sink 103 is connected to the ground. Bases of the transistors Q105 and Q106 are connected to the collectors of the transistors Q102 and Q101 serving as output terminals of the first balanced differential pair, respectively.
Here, a differential output current .DELTA.I.sub.C, which is an amplified output signal of the OTA, is defined as the difference between collector currents I.sub.C105 and I.sub.C106 of the transistors Q105 and Q106, i.e., .DELTA.I.sub.C =I.sub.C105 -I.sub.C106. Then, the differential output current .DELTA.I.sub.C is derived from the collectors of the transistors Q105 and Q106.
Next, the operation of the conventional Gilbert gain cell shows in FIG. 1 is explained below.
Here, supposing that the base-width modulation (i.e., the Early voltage) is ignored and that the common-base current gain factor of a bipolar transistor is equal to unity, a collector current I.sub.C a bipolar transistor is typically given as the following expression (1a). ##EQU1##
In the expression (1a) V.sub.BE is a base-to-emitter voltage of the bipolar transistor, and I.sub.S is the saturation current thereof. Also, V.sub.T is the thermal voltage defined as V.sub.T =kT/q, where k is the Boltzmann's constant, T is absolute temperature in degrees Kelvin, and q is the charge of an electron.
The expression (1a) can be rewritten to the following form (1b). ##EQU2##
When the differential input voltage V.sub.i is applied across the bases of the transistors Q101 and Q102 of the first balanced differential pair, the following relationship (2) is established around the loop consisting of the input voltage and the two base-emitter junctions of the transistors Q101 and Q102 because of the Kirchhoff's voltage law EQU V.sub.i =V.sub.BE101 -V.sub.BE102 +Ri (2)
where V.sub.BE101 and V.sub.BE102 are base-to-emitter voltages of the transistors Q101 and Q102, and i is a current flowing through the common emitter resistor R101.
Supposing that a relationship of Ri&gt;&gt;(V.sub.BE101 -V.sub.BE102) is established, the current i is expressed as follows using the above relationship (2). ##EQU3##
The relationship (3) means that the current i is approximately proportional to the differential input voltage V.sub.i.
The current i flowing through the emitter resistor R101 further flows the diode-connected transistors Q103 and Q104 as a differential current. Thus, if collector currents of the transistors Q101 and Q102 are defined as I.sub.C101 and I.sub.C102, respectively, the collector currents I.sub.C101 and I.sub.C102 are expressed as EQU I.sub.C101 =I.sub.0 +i (4) EQU I.sub.C102 =I.sub.0 -i (5)
Therefore, the following relationships, (6) and (7) are established using the above expression (1b). ##EQU4##
Thus, from the relationships (6) and (7), the difference .DELTA.V.sub.BE between the base-to-emitter voltages V.sub.BE101 and V.sub.BE102 is given by the following expression (8). ##EQU5##
It is seen from the expression (8) that the voltage difference .DELTA.V.sub.BE is in a logarithmically compressed form of the current i. This means that the voltage difference .DELTA.V.sub.BE is logarithmically proportional to the current i.
The voltage difference .DELTA.V.sub.BE is then applied across the bases of the transistors Q105 and Q106 of the second balanced differential pair and is amplified. Thus, the differential output current .DELTA.I.sub.C of the second balanced differential pair, which is an amplified output signal of .DELTA.V.sub.BE, is given as ##EQU6##
The relationship (9) is obtained by the known result that a differential output current .DELTA.I of a balanced differential pair of two emitter-coupled bipolar transistors driven by a constant current I.sub.x is expressed as ##EQU7## where V.sub.IN is a differential input voltage applied across the bases of the two bipolar transistors.
It is seen from the relationship (9) that the differential output current .DELTA.I.sub.C is in an exponentially expanded form of the inputted voltage difference .DELTA.V.sub.BE.
The above relationship (9) is rewritten to the following expression (10a) using the above expression (8). ##EQU8##
This expression (10a) can be further rewritten to as follows. ##EQU9##
Thus, it is seen from the expression (10b) that the output current .DELTA.I.sub.C is proportional to the current i flowing through the emitter resistor R101. This means that the current i can be derived from the collectors of the transistors Q105 and Q106. On the other hand, as described previously with reference to the expression (3), the current i is approximately proportional to the differential input voltage V.sub.i.
Accordingly, the output current .DELTA.I.sub.C is proportional to the differential input voltage V.sub.i. This means that the circuit in FIG. 1 has a linear transconductance and is capable of an OTA function.
With the conventional Gilbert gain cell in FIG. 1, using the above expression (10b) the collector currents I.sub.C105 and I.sub.C106 of the transistors Q105 and Q106 are expressed as the following equations (11) and (12), respectively. ##EQU10##
On the other hand, from the above relationships (4) and (5), collector currents I.sub.C101, and I.sub.C102 of the transistors Q101 and Q102 are expressed as ##EQU11##
Therefore, it is seen from the equations (11), (12), (13), and (14) that the collector currents I.sub.C105 and I.sub.C106 of the transistors Q105 and Q106 are equal to the results obtained by multiplying I.sub.C101 and I.sub.C102 by (I.sub.1 /2I.sub.0), respectively. This means that no improvement is realized for the transconductance linearity in the conventional Gilbert gain cell.
Further, the conventional Gilbert gain call contains the arithmetic approximation as shown in the above equation (3), and as a result, a completely linear transconductance is unable to be realized. Satisfactory linearity in the OTA behavior can be realized only when the value of the resistance R of the emitter resistor R101 and the values of the constant currents I.sub.0 and I.sub.1 are suitably designed.
A significant problem of the conventional Gilbert gain cell is that the signal-to-noise ratio (S/N) is remarkably degraded, which is due to the logarithmic compression and exponential expansion of the input voltage V.sub.i.
An OTA is an essential, basic function block in analog signal applications. Recently, fabrication processes for large-scale integrated circuits (LSIs) have been becoming finer and finer and as a result, the supply voltage for the LSIs has been decreasing from 5 V to 3 V, or lower. This tendency has been lowering the input signal level and necessitating the higher S/N level.